Analysis on Credit card customers

Preparing the data

You should consider writing a function whenever you’ve copied and pasted a block of code more than twice (i.e. you now have three copies of the same code). For example, take a look at this code. What does it do?

data <- as.data.frame(read.csv("/Users/anumehamishra/Desktop/BankChurners.csv", header=T, sep=",", na.strings = c("","NA")))
head(data)

##   CLIENTNUM    Attrition_Flag Customer_Age Gender Dependent_count
## 1 768805383 Existing Customer           45      M               3
## 2 818770008 Existing Customer           49      F               5
## 3 713982108 Existing Customer           51      M               3
## 4 769911858 Existing Customer           40      F               4
## 5 709106358 Existing Customer           40      M               3
## 6 713061558 Existing Customer           44      M               2
##   Education_Level Marital_Status Income_Category Card_Category Months_on_book
## 1     High School        Married     $60K - $80K          Blue             39
## 2        Graduate         Single  Less than $40K          Blue             44
## 3        Graduate        Married    $80K - $120K          Blue             36
## 4     High School        Unknown  Less than $40K          Blue             34
## 5      Uneducated        Married     $60K - $80K          Blue             21
## 6        Graduate        Married     $40K - $60K          Blue             36
##   Total_Relationship_Count Months_Inactive Contacts_Count Credit_Limit
## 1                        5               1              3        12691
## 2                        6               1              2         8256
## 3                        4               1              0         3418
## 4                        3               4              1         3313
## 5                        5               1              0         4716
## 6                        3               1              2         4010
##   Total_Revolving_Bal Total_Amt_Chng_Q4_Q1 Total_Trans_Amt Total_Trans_Ct
## 1                 777                1.335            1144             42
## 2                 864                1.541            1291             33
## 3                   0                2.594            1887             20
## 4                2517                1.405            1171             20
## 5                   0                2.175             816             28
## 6                1247                1.376            1088             24
##   Total_Ct_Chng_Q4_Q1 Avg_Utilization_Ratio
## 1               1.625                 0.061
## 2               3.714                 0.105
## 3               2.333                 0.000
## 4               2.333                 0.760
## 5               2.500                 0.000
## 6               0.846                 0.311

Analyzing the data

PART 1

Categorical 1- Finding the number of males and females customers

table(data$Gender)

## 
##    F    M 
## 5358 4769

barplot(table(data$Gender), col = "cyan", ylim = c(0,6000), las = 2, xlab = "Gender",ylab = "Number of customers")

Finding the martial status distributions of the customers

table(data$Marital_Status)

## 
## Divorced  Married   Single  Unknown 
##      748     4687     3943      749

barplot(table(data$Marital_Status), col = "cyan", ylim = c(0,5000), las = 2, xlab = "Marital_Status",ylab = "Number of customers")

Numerical 1- Finding the number of males and females customers who have dependents as = 5

Dependents <- data[data$Dependent_count == '5', ]
table(Dependents$Gender)

## 
##   F   M 
## 225 199

barplot(table(Dependents$Gender), col = "red", ylim = c(0,250), density=c(10,20),las = 2, xlab = "Dependents = 5", ylab = "Number of customers")

PART 2

Categorical 2- Calculating distribution of education level among customers

Education_Level <- table(data$Education_Level)
slice.labels <- names(Education_Level)
slice.percents <- round(Education_Level/sum(Education_Level)*100)
slice.labels <- paste(slice.labels, slice.percents)
slice.labels <- paste(slice.labels, "%", sep = "")
pie(Education_Level, labels = slice.labels, col = hcl(c(0, 60, 120)))

PART 3

Numerical - numeric data and analyzing distribution on it

a. Finding the summary of my data on the basis of Age

Boxplot showing the ages of customers

fivenum(data$Customer_Age)

## [1] 26 41 46 52 73

boxplot(data$Customer_Age, horizontal = TRUE, xaxt = "n", xlab = "Age of customers", col=hcl(1))
axis(side = 1, at=fivenum(data$Customer_Age), labels = TRUE)

b. This will show the distribution of status of customers based on thier age.

age_status <- fivenum(data$Customer_Age)
age_status

## [1] 26 41 46 52 73

library(ggplot2)
ggplot(data, aes(x=Customer_Age)) +
  geom_histogram(color="black", fill="blue") + facet_grid(~Attrition_Flag)

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

c- The distriution of age varying with 5 dependents

Dependents <- data[data$Dependent_count == '5',]
head(Dependents)

##     CLIENTNUM    Attrition_Flag Customer_Age Gender Dependent_count
## 2   818770008 Existing Customer           49      F               5
## 11  708790833 Existing Customer           42      M               5
## 59  711427458 Existing Customer           44      F               5
## 74  820582308 Existing Customer           42      M               5
## 141 789322833 Attrited Customer           48      F               5
## 156 713786508 Existing Customer           42      F               5
##     Education_Level Marital_Status Income_Category Card_Category Months_on_book
## 2          Graduate         Single  Less than $40K          Blue             44
## 11       Uneducated        Unknown         $120K +          Blue             31
## 59         Graduate        Married         Unknown          Blue             35
## 74       Uneducated        Married    $80K - $120K          Blue             37
## 141     High School        Married  Less than $40K          Blue             38
## 156         Unknown        Married     $40K - $60K          Blue             36
##     Total_Relationship_Count Months_Inactive Contacts_Count Credit_Limit
## 2                          6               1              2         8256
## 11                         5               3              2         6748
## 59                         4               1              2         6273
## 74                         6               2              2        22913
## 141                        1               3              3         8025
## 156                        3               3              3         2038
##     Total_Revolving_Bal Total_Amt_Chng_Q4_Q1 Total_Trans_Amt Total_Trans_Ct
## 2                   864                1.541            1291             33
## 11                 1467                0.831            1201             42
## 59                  978                2.275            1359             25
## 74                 1528                0.414            1394             35
## 141                   0                0.654             673             18
## 156                   0                0.786            1238             28
##     Total_Ct_Chng_Q4_Q1 Avg_Utilization_Ratio
## 2                 3.714                 0.105
## 11                0.680                 0.217
## 59                1.083                 0.156
## 74                0.522                 0.067
## 141               0.800                 0.000
## 156               0.750                 0.000

A <- Dependents$Customer_Age
B <- Dependents$Customer_Age
boxplot(A,B, xaxt = "n", xlab = "variations of age with 5 dependents", ylab = "Age of Customers", col=c("yellow", "green"))

d- Scatter Plot- Showing age of the customers, count of Dependents and the count of transactions

data2=data.frame(Age=data$Customer_Age,Dependent=data$Dependent_count,Transactions=data$Total_Trans_Ct)
head(data2,10)

##    Age Dependent Transactions
## 1   45         3           42
## 2   49         5           33
## 3   51         3           20
## 4   40         4           20
## 5   40         3           28
## 6   44         2           24
## 7   51         4           31
## 8   32         0           36
## 9   37         3           24
## 10  48         2           32

plot(data2 , pch=20 , cex=1.0 , col="lightblue")

e- Plotted a ggplot for age vs Dependent_count, and we have the points colored based on Education_Level

ggplot(data = data) +
  geom_point(mapping = aes(x = Customer_Age, y = Dependent_count, colour = Education_Level ))

library(plotly)

## 
## Attaching package: 'plotly'

## The following object is masked from 'package:ggplot2':
## 
##     last_plot

## The following object is masked from 'package:stats':
## 
##     filter

## The following object is masked from 'package:graphics':
## 
##     layout

f - Mixed plot of age, months on book in the bank and contacts made by each customer

a <- plot_ly(data, x = data$Customer_Age, type="box", name = 'age')
b <-add_trace(a, x = data$Months_on_book, type="box", name = 'Months')
c <-add_trace(b , x = data$Contacts_Count,type = "box" , name ="Contacts_made" )
c

## Warning: `arrange_()` is deprecated as of dplyr 0.7.0.
## Please use `arrange()` instead.
## See vignette('programming') for more help
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.

g - Analysis of distribution on Customers Age

values <- data$Customer_Age
tab <- table(values)
dframe <- as.data.frame(tab)
dframe

##    values Freq
## 1      26   78
## 2      27   32
## 3      28   29
## 4      29   56
## 5      30   70
## 6      31   91
## 7      32  106
## 8      33  127
## 9      34  146
## 10     35  184
## 11     36  221
## 12     37  260
## 13     38  303
## 14     39  333
## 15     40  361
## 16     41  379
## 17     42  426
## 18     43  473
## 19     44  500
## 20     45  486
## 21     46  490
## 22     47  479
## 23     48  472
## 24     49  495
## 25     50  452
## 26     51  398
## 27     52  376
## 28     53  387
## 29     54  307
## 30     55  279
## 31     56  262
## 32     57  223
## 33     58  157
## 34     59  157
## 35     60  127
## 36     61   93
## 37     62   93
## 38     63   65
## 39     64   43
## 40     65  101
## 41     66    2
## 42     67    4
## 43     68    2
## 44     70    1
## 45     73    1

x <- as.numeric(as.character(dframe$values))
x

##  [1] 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
## [26] 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 70 73

The probability distribution is:

f <- dframe$Freq / (sum(dframe$Freq))

The mean:

mu <- sum(x * f)
mu

## [1] 46.32596

Variance of the distribution is:

sigmaSquare <- sum((x - mu)^2 * f)
sigmaSquare

## [1] 64.26296

sigma <- sqrt(sigmaSquare)
sigma

## [1] 8.016418

Showing probability distribution of age:

plot(x, f, type = 'h', xlab = "Age", ylab = "PMF", ylim = c(0, 0.06), main
     = "Spike plot for Age")
abline(h = 0 )

Showing cumulative distribution of age:

cdf <- c(0, cumsum(f))
cdfplot <- stepfun(x, cdf)
plot(cdfplot, verticals=FALSE, pch=16, main="CDF Plot for Age", xlab = "Age", ylab = "C
DF")

h - Analysis on the distribution of Customer’s income

values2 <- data$Dependent_count
tab <- table(values2)
dframe <- as.data.frame(tab)
dframe

##   values2 Freq
## 1       0  904
## 2       1 1838
## 3       2 2655
## 4       3 2732
## 5       4 1574
## 6       5  424

x <- as.numeric(as.character(dframe$values2))
x

## [1] 0 1 2 3 4 5

The probability distribution is:

f <- dframe$Freq / (sum(dframe$Freq))

The mean:

mu <- sum(x * f)
mu

## [1] 2.346203

The variance of the distribution is:

sigmaSquare <- sum((x - mu)^2 * f)
sigmaSquare

## [1] 1.686996

sigma <- sqrt(sigmaSquare)
sigma

## [1] 1.298844

Showing probability distribution of Income category:

plot(x, f, type = 'h', xlab = "Income_Category", ylab = "PMF", ylim = c(0, 0.5), main
     = "Spike plot for Income")
abline(h = 0 )

Showing cumulative distribution of Income category

cdf <- c(0, cumsum(f))
cdfplot <- stepfun(x, cdf)
plot(cdfplot, verticals=FALSE, pch=16, main="CDF Plot for Income", xlab = "Age", ylab = "C
DF")

PART 4- Central Limit Theorem

Applying Central Limit Theorem on age

Age <-data$Customer_Age
ctable <- table(Age)

The mean is :

mu <- mean(Age)
mu

## [1] 46.32596

sigma <- sd(Age)
sigma

## [1] 8.016814

Histogram showing the age of the customers:

dframe <- as.data.frame(ctable)
x <- as.numeric(as.character(data$Customer_Age))
head(x)

## [1] 45 49 51 40 40 44

hist(x, probability = TRUE, xlim = c(0, 80), xlab = "Age", ylab = "Density", main = "Histogram of age")

Showing results with sample size 5

samples <- 1000
sample_size <- 5
xbar <- numeric(samples)
for(i in 1:samples){
  xbar[i] = mean(sample(x, size = sample_size, replace = T))
}
hist(xbar, prob = T, xlab = "Age",
     main = "Densities of age with sample size 5", col = "purple")

Mean:

mean1 <- mean(xbar)
mean1

## [1] 46.3198

Standard deviation

sd1 <- sd(xbar)
sd1

## [1] 3.640844

Showing results with sample size 20

samples <- 1000
sample_size <- 20
xbar <- numeric(samples)
for(i in 1:samples){
  xbar[i] = mean(sample(x, size = sample_size, replace = T))
}
hist(xbar, prob = T, xlab = "Age",
     main = "Densities of age with sample size 20", col = "red")

Mean:

mean2 <- mean(xbar)
mean2

## [1] 46.2087

Standard deviation

sd2 <- sd(xbar)
sd2

## [1] 1.781045

Showing results with sample size 50

samples <- 1000
sample_size <- 50
xbar <- numeric(samples)
for(i in 1:samples){
  xbar[i] = mean(sample(x, size = sample_size, replace = T))
}
hist(xbar, prob = T, xlab = "Age",
     main = "Densities of age with sample size 50", col = "brown")

Mean:

mean3 <- mean(xbar)
mean3

## [1] 46.31612

Standard deviation

sd3 <- sd(xbar)
sd3

## [1] 1.104157

cat("1st distribution:\nMean =",mean1,"\nSD =",sd1)

## 1st distribution:
## Mean = 46.3198 
## SD = 3.640844

cat("2nd distribution:\nMean =",mean2,"\nSD =",sd2)

## 2nd distribution:
## Mean = 46.2087 
## SD = 1.781045

cat("3rd distribution:\nMean =",mean3,"\nSD =",sd3)

## 3rd distribution:
## Mean = 46.31612 
## SD = 1.104157

INFERENCE: As we change our sample space and keep increasing it, we notice that the mean almost remains the same whereas the Standard deviation decreases hence proving the property of Central Limit Theorem

PART 5- Sampling

library(sampling)
table(data$Customer_Age)

## 
##  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45 
##  78  32  29  56  70  91 106 127 146 184 221 260 303 333 361 379 426 473 500 486 
##  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  64  65 
## 490 479 472 495 452 398 376 387 307 279 262 223 157 157 127  93  93  65  43 101 
##  66  67  68  70  73 
##   2   4   2   1   1

hist(data$Customer_Age,col="yellow")

Using sampling methods for sample size of 200

Without replacement

sample.size <- 200
s <- srswor(sample.size,nrow(data))
sample.1 <- data[s != 0, ]
mean_srswor <- mean(sample.1$Customer_Age)
set.seed(153)

With replacement

s <- srswr(sample.size, nrow(data))
sample.2 <- data[s != 0, ]
mean_srswr <- mean(sample.2$Customer_Age)
set.seed(123)

Systematic Sampling

N <- nrow(data)
n <- 200

items in each group

k <- ceiling(N / n)
k

## [1] 51

random item from first group

r <- sample(k, 1)
r

## [1] 31

selecting every kth item

s <- seq(r, by = k, length = n)
head(s)

## [1]  31  82 133 184 235 286

sample.3 <- data[s, ]
table(sample.3$Customer_Age)

## 
## 27 28 29 31 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 
##  1  1  2  1  4  4  3  4  7  8  8  2 11 12  8 12  8  7  5 17  8  6  4  9  5  3 
## 55 56 57 58 59 60 61 62 64 65 
##  4 10  6  3  2  2  5  2  1  3

mean_systematic <- mean(sample.3$Customer_Age)
mean_systematic

## [1] NA

Systematic sampling with unequal probabilities

pik <- inclusionprobabilities(data$Customer_Age, sample.size)
s <- UPsystematic(pik)
sample.4 <- data[s != 0, ]
table(sample.4$Customer_Age)

## 
## 26 27 28 30 31 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 
##  1  1  2  4  2  2  2  3  5  3  3  5  5  7  4 16 10 10  7 10 10  9  8  7 12  8 
## 54 55 56 57 58 59 60 62 64 65 67 
##  9  4  6 10  3  3  2  2  1  3  1

Stratified Sampling

data["age_range"] = NA
data$age_range <- cut(data$Customer_Age, breaks = c(0, 25, 50, 75, Inf), labels = c('A', 'B', 'C','D'))
data_age <- data.frame(
  Customer_Age = data$Customer_Age,
  age_range = data$age_range
)
freq <- table(data_age$age_range)
freq

## 
##    A    B    C    D 
##    0 7049 3078    0

set.seed(123)
head(data_age)

##   Customer_Age age_range
## 1           45         B
## 2           49         B
## 3           51         C
## 4           40         B
## 5           40         B
## 6           44         B

Cluster sampling

cl <- cluster(data, c("Customer_Age"), size = 4, method = "srswor")
sample.6 <- getdata(data, cl)
table(sample.6$Customer_Age)

## 
##  28  39  40  56 
##  29 333 361 262

mean_cluster <- mean(sample.6$Customer_Age)
mean_cluster

## [1] 43.56447

Mean without replacement

mean_srswor

## [1] 45.82

Mean with replacement

mean_srswr

## [1] 46.0603

Systematic Mean

mean_systematic

## [1] NA

Using sampling methods for sample size of 700

Without replacement

sample.size <- 700
s <- srswor(sample.size,nrow(data))
sample.1 <- data[s != 0, ]
mean_srswor <- mean(sample.1$Customer_Age)

With replacement

set.seed(153)
s <- srswr(sample.size, nrow(data))
sample.2 <- data[s != 0, ]
mean_srswr <- mean(sample.2$Customer_Age)

Systematic Sampling

N <- nrow(data)
n <- 700

items in each group

k <- ceiling(N / n)
k

## [1] 15

random items in first group

r <- sample(k, 1)
r

## [1] 10

selecting every kth item

s <- seq(r, by = k, length = n)
head(s)

## [1] 10 25 40 55 70 85

sample.3 <- data[s, ]
table(sample.3$Customer_Age)

## 
## 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 
##  5  2  3  1  7  3  7  4 15  6 10 20 21 23 21 33 29 21 38 40 36 27 38 32 26 23 
## 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 
## 21 27 22 12 18 18 18 11 11  7  5  4  2  7  1

mean_systematic <- mean(sample.3$Customer_Age)

Systematic Sampling with unequal probabilities

pik <- inclusionprobabilities(data$Customer_Age, sample.size)
s <- UPsystematic(pik)
sample.4 <- data[s != 0, ]
table(sample.4$Customer_Age)

## 
## 26 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 
##  2  1  5  5  3  5  9  8 16 12 19 16 18 17 20 23 34 27 42 26 36 36 42 39 35 25 
## 53 54 55 56 57 58 59 60 61 62 63 64 65 67 
## 20 23 29 26 14  8 14 10 12  9  2  3  8  1

Stratified sampling

freq <- table(data_age$age_range)
freq

## 
##    A    B    C    D 
##    0 7049 3078    0

set.seed(123)
head(data_age)

##   Customer_Age age_range
## 1           45         B
## 2           49         B
## 3           51         C
## 4           40         B
## 5           40         B
## 6           44         B

Cluster mean

mean_cluster

## [1] 43.56447

Systematic mean

mean_systematic

## [1] NA

Mean With replacement

mean_srswr

## [1] 46.47563

Mean Without replacement

mean_srswor

## [1] 46.24

Analysis on Credit card customers

Introduction

Objective

Preparing the data

Analyzing the data

PART 1

Categorical 1- Finding the number of males and females customers

Finding the martial status distributions of the customers

Numerical 1- Finding the number of males and females customers who have dependents as = 5

PART 2

Categorical 2- Calculating distribution of education level among customers

PART 3

Numerical - numeric data and analyzing distribution on it

a. Finding the summary of my data on the basis of Age

Boxplot showing the ages of customers

b. This will show the distribution of status of customers based on thier age.

c- The distriution of age varying with 5 dependents

d- Scatter Plot- Showing age of the customers, count of Dependents and the count of transactions

e- Plotted a ggplot for age vs Dependent_count, and we have the points colored based on Education_Level

f - Mixed plot of age, months on book in the bank and contacts made by each customer

g - Analysis of distribution on Customers Age

h - Analysis on the distribution of Customer’s income

PART 4- Central Limit Theorem

Applying Central Limit Theorem on age

Showing results with sample size 5

Showing results with sample size 20

Showing results with sample size 50

INFERENCE: As we change our sample space and keep increasing it, we notice that the mean almost remains the same whereas the Standard deviation decreases hence proving the property of Central Limit Theorem

PART 5- Sampling

Using sampling methods for sample size of 200

Without replacement

With replacement

Systematic Sampling

items in each group

random item from first group

selecting every kth item

Systematic sampling with unequal probabilities

Stratified Sampling

Cluster sampling

Mean without replacement

Mean with replacement

Systematic Mean

Using sampling methods for sample size of 700

Without replacement

With replacement

Systematic Sampling

items in each group

random items in first group

selecting every kth item

Systematic Sampling with unequal probabilities

Stratified sampling

Cluster mean

Systematic mean

Mean With replacement

Mean Without replacement